Could my engine be damaged

That is certainly not good for your engine, but it's hard to say how much damage has been done. With some luck your car will be fine. Don't drive it again until you refill the oil obviously. Check the oil weekly until you have more confidence around how often you need to check it.

Change the oil as soon as possible and check how much metal debris is in the oil. A good mechanic can tell you if there is an abnormal amount. If there is excessive metal int he oil, damage may have occurred. If there is no excess metal, I would say if the car runs fine, do not worry about the incident.

My brother let the oil drop too low on an old car 35 years ago. After driving it for a few days, it permanently made a knocking sound while sitting at the stop lights. A mechanic said it was damaged wrist pins. I can't say how long the engine lasted because my family sold it shortly thereafter.